Tuesday, October 13, 2015

Exploding dice on low values

Why do exploding dice seldom explode on low values? We're all used to d10s exploding on 10 and so forth. Question is, why don't they explode on 1s? More so, what's the value of them exploding on 1s, 2s, 3s, etc.? You get the idea, exploding on low values.

On the up side it makes a lot of sense to have a d10 explode on a 10 and keep exploding on and on. It really fuels the player's emotions and adds to the excitement. On the down side it keeps the players with the low values. You roll a 1 and a 10 you get to roll the 10 again, but you're stuck with the one. You might turn that 10 into a ten again, but I'm quite confident you'll get some lower value 9 out of 10 times.

Now, what happens when when what we roll again are low values? Lets say I rolled a 10 and a 1. I get to roll the one again. Obviously it can't get any worse and can only get better, right? I might get a 10 or a 2, either way it's better than keeping the one and I already had a 10.

Of course it requires me to roll low to get another roll. So I can inch myself up to higher valued rolls by adding 1 at a time. This of course doesn't sound as exciting as leaping across values at a rate of ten points at a time. A d10 that explodes on a 10 adds 10 for every time it does explode, whereas a d10 that explodes adds 1 for every time it does explode. So to add 10 points I'd have to make it explode 10 times. A rather uncommon feat I may add.

So it begins to become clear why exploding dice don't tend to explode on low values. It's slow and boring to get a bonus from them. Unless of course the value required to explode increases with level.

Let us imagine a game with five skill levels: unskilled, experienced, expert, master and legendary. Characters who are unskilled at something roll without exploding dice, experienced characters' dice explode on a 1, expert dice explode on a 2, master on a 3 and legendary on a 4. Now lets imagine that all skill rolls are made with 3d10 (you know to have a nice bell curve). While an unskilled character might get a 3 a legendary character can never get less than 15 (3x5) since any 4 or lower value would trigger another roll.

I ran a small program with low exploding 3d6 on anydice and got the following graph. I used d6 to keep the numbers small and the graphs from scrolling sideways. The behavior is nevertheless very similar with d10.

The four curves on the right are the rolls for 3d6 exploding dice for the master (black, explode on 1,2,3, or 4), expert (orange, explode on 1,2, or 3), experienced (cyan, explode on 1 or 2) and novice (green, explode on 1). It is clear to see how the curves move right as skill increases. The dice mechanism prevents skilled characters from rolling too low, which is something we'd expect out of a skilled character, right?

The four curves to the left are opposing die rolls using the four skill levels against an expert. As you can see the yellow curve is slightly to the right of zero. This indicates the expected advantage a master should have over an expert. The blue curve is centered on zero and represents the odds of an expert vs an expert. The other two curves (red and pink) land to the left of zero, showing the advantage experts have over the two lower skill levels. Opposing die rolls would tend to fall below zero in a clear disadvantage to the lesser skilled characters.

So low value exploding dice may not be as exciting as high value exploding dice, but they sure make for a nice and simple skill mechanism that is easy to understand and implement in the game. Thoughts?

You can see the actual script for the low exploding d6 by following this link.
http://anydice.com/program/6ccd

In contrast to the low exploding d6 you can see the high exploding d6 here. These explode on values >=6, >=5 and >=4.

As you can see the curve moves a bit towards the right as the skill increases, but they all start at 3. Meaning that no matter how skilled a character is the odds for a low value are the same as any lesser skilled character.